Question

A fly undergoes a displacement of -5. 80 m while accelerating at -1. 33 m/s for 4. 22 s what was the initial velocity of the fly.

Answer 1

The fly has an average velocity of

v[ave] = ∆x/∆t = (-5.80 m) / (4.22 s) ≈ -1.37 m/s

If its acceleration is constant, then its average velocity is also equal to the average of its initial and final velocities,

v[ave] = (v[initial] + v[final]) / 2

which tells us that

v[initial] ≈ -1.37 m/s - 1/2 v[final]

The fly's final velocity after some time t is given by

v[final] = v[initial] + (-1.33 m/s²) t

so that after 4.22 s, we have

v[final] ≈ v[initial] - 5.61 m/s

Substitute this into the equation for v[initial] :

v[initial] ≈ -1.37 m/s - 1/2 (v[initial] - 5.61 m/s)

Solve for v[initial] :

3/2 v[initial] ≈ -1.37 m/s + 1/2 (5.61 m/s)

⇒ v[initial] ≈ 0.955 m/s